SOME APPLICATIONS OF GENERALIZED RUSCHEWEYH DERIVATIVES
INVOLVING A GENERAL FRACTIONAL DERIVATIVE OPERATOR TO A CLASS OF ANALYTIC
FUNCTIONS WITH NEGATIVE COEFFICIENTS I

Waggas Galib Atshan and S. R. Kulkarni

Abstract. For certain univalent function f, we
study a class of functions f as defined by making use of the generalized
Ruscheweyh derivatives involving a general fractional derivative operator,
satisfying

A necessary and sufficient condition for a function to be in the class Aγλ, μ, ν(n, β) is obtained. In addition, our paper
includes distortion theorem, radii of starlikeness, convexity and
close-to-convexity, extreme points. Also, we get some results in this paper.